In the Byzantine version of basketball, there are just two ways to score: by making a free throw, or by making a field goal. A field goal is worth more points than a free throw. Over the years, scorekeepers for Byzantine basketball have noticed that there are 35 different game scores that have never been reached. In fact, they can't be reached. One of these impossible scores is 58.
What is the value of a free throw?
The Ruthenian Post Office issues stamps in just three denominations: 6 crocs, 9 crocs, and 20 crocs. Since Ruthenia is short of currency, it is common to pay for some items using postage stamps. Obviously, you can't pay for anything that costs less than 6 crocs in this way. It should be almost as obvious that 7, 8, 10 and 11 crocs cannot be formed using postage stamps.
What is the largest value that cannot be formed using Ruthenian postage stamps?
I give up, show me the solution.
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